#help-26
topaz sinewBOT
acoustic pecan
have you done row reduction
topaz sinewBOT
@gritty moon Has your question been resolved?
topaz sinewBOT
topaz sinewBOT
Available help channel!
narrow ember
just need confirmation to see if my answer is correct. my previous answer was 100*(sqrtA/P-1). the one down below is my new answer
topaz sinewBOT
just need confirmation to see if my answer is correct. my previous answer was 10...
acoustic pecan
seems good
narrow ember
seems good
they marked it as wrong
narrow ember
maybe try getting rid of the brackets in A/P
did that too and got it wrong lol
empty sail
I'm assuming because $x^2 = a \to \sqrt{x^2} = \pm \sqrt{a}$
thorny flameBOT
dldh06
empty sail
Meaning it's plus/minus
acoustic pecan
aha, yeah it does say answers rather than answer
narrow ember
what do i put in im confused lol i only got one more submission left
empty sail
A comma separated list
narrow ember
A comma separated list
can you type it down for me pls?
empty sail
**dldh06**
.
You have one of the answers
You need the other one
You separate both answers with a comma
narrow ember
You separate both answers with a comma
Oh i see
can you help me get the other answer?
@empty sail
empty sail
I told you how
empty sail
**dldh06**
.
narrow ember
should i put in the answer i have and the one u wrote down?
empty sail
$\pm \sqrt{a}$ means $+\sqrt{a}$ and $-\sqrt{a}$
thorny flameBOT
dldh06
narrow ember
$\pm \sqrt{a}$ means $+\sqrt{a}$ and $-\sqrt{a}$
So, is this right?:
i = 100 * (sqrt(A/P) - 1)
i = -100 * (sqrt(A/P) - 1)
@empty sail how is this?
topaz sinewBOT
@narrow ember Has your question been resolved?
narrow ember
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
modest thistle
Can someone help me on how to find a discriminant from 28a³/3 + 12a² - 16 = 0?
modest thistle
and should i use the D = b²-4ac formula or the -b±√b²-4ac/2a?
raw mirage
is the question to solve for a?
modest thistle
is the question to solve for a?
wait, let me check again
raw mirage
Besides,in the 4th line you've written -9(3a) as -12a, should be -27a
modest thistle
Besides,in the 4th line you've written -9(3a) as -12a, should be -27a
I'm sorry, my english isn't that good. Can you mark it by giving me photo here?
raw mirage
wait that's a 4 im blind
is the integrand is x²+3x-4 or x²+3x-9 lmao im too blind to see
modest thistle
is the integrand is x²+3x-4 or x²+3x-9 lmao im too blind to see
its x²-3x-4
sorry my handwriting is bad
raw mirage
the final equation 28a³/3 + 12a²-16a=0 seems to be corect if its a 4
use the quadratic formula -b±√(b²-4ac)/2a to get the roots after you factor out an a
modest thistle
use the quadratic formula -b±√(b²-4ac)/2a to get the roots after you factor out ...
okay. So the for the indicator, a is 28/3, b is 12, c is 16 and then i just have to input the formula right?
raw mirage
c is -16
modest thistle
oh yes, sorry. My bad
raw mirage
also it would be better if you multiply by 3 to get 28a²+36a-48 and then simplify it by dividing by 4
wouldn't have to calculate with large values Android fractions
modest thistle
also it would be better if you multiply by 3 to get 28a²+36a-48 and then simplif...
so that's mean the a is 28 b is 36 and c is -48
raw mirage
if u divide by 4, you get 7a²+9a-12
this is the simplest form
here a is 7, b is 9 and c is -12
modest thistle
here a is 7, b is 9 and c is -12
okay. Now i just have to input the formula
raw mirage
yeah
modest thistle
oh so it's a positive then
raw mirage
81+336
raw mirage
oh so it's a positive then
yea
raw mirage
-9±√417/14<@645916238949777408>
2 from this
remember the a you factored out
in the beginning
that gives a=0
its a cubic, there are 3 values of a
modest thistle
hmm let me understand it first
modest thistle
remember the a you factored out
the 28a³/3 right?
that we multiply by 3 the others and after that all of it got divided by 4
raw mirage
yeah it was 28a³/3 + 12a² - 16a=0
factor out an a from the three terms
a(28a²/3 + 12a - 16)=0
this gives a=0 or 28a²/3+12a-16
we solved the other quadratic by multiplying by 3 and dividing by 4
modest thistle
this gives a=0 or 28a²/3+12a-16
we solved the other quadratic by multiplying by ...
okay, and after we divided it into 7a²+9a-12=0 the a in this number there are three, so does it mean the a is three then or is it not like that?
raw mirage
a is the not 3, there are just 3 different values for a
that's what im saying, a=0 is also a solution
modest thistle
that's what im saying, a=0 is also a solution
ah i see. So the final conclusion is a=0?
3 values a, a=0
raw mirage
the final conclusion is that a=0, (-9+√417)/14 and (-9-√417)/14
raw mirage
it'd be better if you factor out the a instead of writing (dividided by a)
modest thistle
it'd be better if you factor out the a instead of writing (dividided by a)
it's 4 sorry, and let me change it to factored by 4
it looks like a lol, but it's 4 my bad
raw mirage
28a³+36a²-48=0
a(28a²+36a-48)=0
a=0 or 28a²+36a-48=0
and then solve the quadratic
writing it like that makes more sense
modest thistle
okay
let me submit it first
@raw mirage and this is already a discriminant right?
just want to reassure
modest thistle
oh okay
let me submit it wait
@raw mirage can we simplify the discriminant?
and also, where's the x1 a d x2 sorry?
can we make the √417 into 20.42?
-9+20.42/14
cinder bloom
(-9±√417)/14 maybe?
cinder bloom
i dont think a math quz should force the root of what into a demical
so better not to write √417 as 20.42
modest thistle
alright, so that's mean it's -9±√417
cinder bloom
yes,and u cant simplify √417 any longer
modest thistle
yes,and u cant simplify √417 any longer
okay, noted
cinder bloom
because 417=3x139 and 139 is a prime number
cinder bloom
...
modest thistle
it's either that or the -9±20.42/14
this one then
cinder bloom
perfect
modest thistle
keep on bro
thanks bro/sis, you too
thanks for helping @cinder bloom @raw mirage
appreciate yall so much
topaz sinewBOT
Available help channel!
finite patrol
Hello. Say we wanted to prove the following statement $\forall a \in \mathbb{Z}, a \in A \Longrightarrow a \geq -1$ for $A = {1, 2, 3, 4}$. Is this proof alright?
Fix an arbitrary $a \in \mathbb{Z}$. Assume $a \in A$, this means $a \geq \min A = 1$, but note that since $\min A = 1 > -1$ then $a \geq \min A > -1$. Thus we've shown that for all $a \in A$, $a > -1$.
This seems problematic to me in some sense. The right side of the implication expands to $a > -1 \lor a = -1$. Although $a >-1$ makes the implication true (is this all we want to do?), we still haven't shown that $a = -1$ is a possibility. Well, it clearly isn't a possibility in this case, but it feels like if I don't somehow show that both $P_1$ and $P_2$ are possible in $X \Longrightarrow P_1 \lor P_2$, I'm doing something wrong.
topaz sinewBOT
Hello. Say we wanted to prove the following statement $\forall a \in \mathbb{Z},...
thorny flameBOT
tejveer
topaz sinewBOT
@finite patrol Has your question been resolved?
knotty ledge
You only need one statement to be true in an OR statement for the OR statement to be true
molten wren
hi
molten wren
if a^2 + b^2 + c^2 = ab+bc+ac
what is
(3a^3 + 2b^3 + c^3)/(abc)
it's a silly question and I solved it before but rn I can't
molten wren
if a^2 + b^2 + c^2 = ab+bc+ac
I tired divding both sides by abc
so
a/bc + b/ac + c/ab = 1/a + 1/b + 1/c
mellow arrow
$a^{3}+b^{3}+c^{3}-3abc=\left(a+b+c\right)\left(a^{2}+b^{2}+c^{2}-ab-bc-ca\right)$
thorny flameBOT
B-eard
mellow arrow
yes
mellow arrow
if a^2 + b^2 + c^2 = ab+bc+ac
Okay, so multiply this equation by 2
and see the magic
topaz sinewBOT
topaz sinewBOT
Available help channel!
undone flicker
topaz sinewBOT
undone flicker
I want to find points only
Rest i have solved the question
I know it will pass through 0,0 and a,9
pulsar sun
tribhuj is triangle?
undone flicker
Yes boss
pulsar sun
k
undone flicker
@noble laurel so gya kya
thorny flameBOT
2 members found matching austinu!
1. Austin (@austinu)
2. austinurbana (@austinurbana)```
Please type the number corresponding to your selection, or type `c` now to cancel.,ti @noble laurel
thorny flameBOT
The current time for austinu is 08:50 AM (PDT) on Sat, 23/09/2023.
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pulsar sun
ye possible hes sleeping
pulsar sun
ek second y^2 - 9xy + 18x^2 = 0 circle nhi hoga?
undone flicker
Quadratic complicated ban rha h
thorny flameBOT
pulsar sun
han wahi but how
$y^2 - 9xy + 18x^2 = y^2 -6xy + 9x^2 + 9x^2 -2xy = (3x-y)^2 + 9x^2 - 2xy$
(3x-y)^2 +x(9x-2y) = 0
undone flicker
Determinant is 0 here so lines
thorny flameBOT
ItzKraken
undone flicker
pulsar sun
ACHHA YEH
ise family of curve nhi kehte ???
maine to yeh nhi seekha hai
maf karo bhaiya madad nhi kr skta
pulsar sun
okay sochne de thoda
undone flicker
Apn ko point niklan h bas
undone flicker
Utna muskil ni h ho gya
thorny flameBOT
ItzKraken
pulsar sun
so $y = \frac{9x \pm 3x}{2}$
thorny flameBOT
ItzKraken
pulsar sun
so $y=6x$ or $y=3x$
thorny flameBOT
ItzKraken
topaz sinewBOT
@undone flicker Has your question been resolved?
mellow arrow
ek second y^2 - 9xy + 18x^2 = 0 circle nhi hoga?
x^2 aur y^2 ka coeff same hona chahiye uske liye
undone flicker
x^2 aur y^2 ka coeff same hona chahiye uske liye
X^2
mellow arrow
plug in y=9 in the first question to get two values of x. these would be two vertices. now for the third vertex, solve the equation 1 for y
you get y=6x or y=3x. their intersection point would be (0,0) which is the tjord vertex
undone flicker
Maine toh y=9 put kiya seeda aur usko solve karke nikal liye
undone flicker
0,0 satisfied equation so it's 3rd one
undone flicker
tisra ke liye equation solve kro
Kaisa equation bro
mellow arrow
y^2-9xy+18x^2=0
undone flicker
Isko maine shuru m 0,0 put kiya
mellow arrow
0,0 satisfy kr rha to koi gurantee nhi ki dono lines ka intersection point yhi hai
us equation ko to (3,9) b satisfy kr rha
pr wo nhi hai intersection point
undone flicker
3,9 hain toh point
undone flicker
Samajh gya ab
Ha lekin ek idea le sakte the vaise
3,9 and 1.5,9 aa rha h points
Toh mtlb ye dono toh y=9 par h
.close
coral fog
Can I get the 3 of -4/3 out like this?
topaz sinewBOT
Can I get the 3 of -4/3 out like this?
coral fog
radiant tapir
,rccw
thorny flameBOT
radiant tapir
no unfortunately no, not unless 1/3 is a factor
like if it was 1/3x - 4/3, then you could
radiant tapir
yeah you could. Not sure how much that'd help here though
versed cairn
the question is to take 1/3 out , not how its useful
radiant tapir
also, you don't get rid of it per se, it moves outside of the integral. It's still part of the quation
radiant tapir
the question is to take 1/3 out , not how its useful
it wasn't actually. OP was asking if what he did was valid. The answer is no
coral fog
How do i get rid of it then
radiant tapir
How do i get rid of it then
there's no getting "rid of it" in this case. Yout can do what JustToPro suggested and do the LCM, then youll be left with this
$\int \frac{x - \frac{4}{3}}{x^2 + x + 1} dx = \int \frac{\frac{1}{3}(3x - 4)}{x^2 + x + 1}dx = \frac{1}{3} \int \frac{3x-4}{x^2 + x + 1}dx$
thorny flameBOT
MellowDramaLlama
coral fog
How did my doctor do so
radiant tapir
,rccw
thorny flameBOT
radiant tapir
sorry bro I can't read that
coral fog
💀
radiant tapir
can you post the original problem?
coral fog
Sure
radiant tapir
actually I gotta head out for the day, so post the original problem and hopefully someone else can swing by
versed cairn
did u solve the partial fraction?
thorny flameBOT
coral fog
<@&286206848099549185>
topaz sinewBOT
@coral fog Has your question been resolved?
coral fog
because we have the same denominator we can write them on the same line
then a/b / c
is a/b.c
right?
<@&286206848099549185>
coral fog
so that's how we got 1/3 outside yes?
white ruin
You can take 1/3 common from numerator
coral fog
yes but it's harder for me
white ruin
Yeah
coral fog
damn this problem was rough
white ruin
so that's how we got 1/3 outside yes?
It's cos 1/3 is part of both of the terms so we just took it common and put it outside
white ruin
Oh ok sorry my bad I thought you only needed help with the denominator part earlier haha
Ok so
You can substitute x + 1/2 = u
white ruin
You can substitute x + 1/2 = u
Have you worked with substituting variables like this earlier or do you need more help
coral fog
Like make it u-1/2=x?
white ruin
Yeahh
And now if you differentiate it on both the sides, you'll get du/dx = 1 or du = dx
coral fog
Yes
white ruin
So you know that x = u-1/2 and dx=du
coral fog
Yes
white ruin
Replace x and dx in terms of u and du
and you'll get 1/3 integral [ (u-9/2) / u^2 + 3/4 ]
(Wait idk how to use latex lol sorry)
coral fog
Yes
white ruin
and you'll get 1/3 integral [ (u-9/2) / u^2 + 3/4 ]
(Wait idk how to use latex ...
Did you get to this
white ruin
Yeah ok cool
Now you need to split the numerator in 2 parts
like (a-b)/c = a/c - b/c
white ruin
yeahh but since there's 1/3 in multiplication of the whole integral, we need to also multiply that with 9/2
So we get 1/3*9/2 = 3/2
white ruin
I mean technically all the artistic work is done yea
You need to know integration formula to solve now
white ruin
No problem 💛
white ruin
Ok so there are 5 terms in the second-last line
Do you know how to integrate some of them?
Cos their integrals are written in their order
So if you wanna know how to integrate the 4th term (circled one) then you can actually substitute u^2 = t
And by differentiating, you'' get dt/du = 2u
So dt = 2u*du
So now you can write the u*du in the numerator of that term as dt/2
and denominator of that term becomes t+3/4
coral fog
why did we re-integrate
white ruin
So it reduces down to integrating (1/3)*(dt/2)/(t+3/4)
white ruin
why did we re-integrate
Actually there's a direct formula you can use here but I'm telling you how you can integrate it if you wanna simplify it more
white ruin
so if I want I can replace all the "u's" by "x's"?
Yess
coral fog
what's the formula maybe I took it
thorny flameBOT
LoveBeforeYouDie
coral fog
but they did not get tan inverse
white ruin
No it works when there's no x in the numerator
coral fog
yes
white ruin
tan inv yeah
No no mb ignore this
white ruin
Ok so
white ruin
**LoveBeforeYouDie**
The formula for this resolves to logarithmic function
Like
$1/2*log(x^2+a^2)$
thorny flameBOT
LoveBeforeYouDie
white ruin
Can you send me the formulas that you are taught?
Maybe I could point the right one for you
Or hmm
white ruin
Yeah i know. it's slightly too specific
coral fog
du/u = ln(u)
white ruin
Do you know the log ones
coral fog
No never took them
coral fog
dt = 2u
white ruin
and dt = 2u*du
coral fog
yes
white ruin
So u*du = dt/2
So basically it reduces to
u*du / u^2 + 3/4 = (dt/2) / t
You can take 1/2 outside
And then it becomes 1/2 * dt/t
And also there's already 1/3 outside
So it's 1/31/2dt/t
Oops
1/3*1/2*dt/t
white ruin
Yeahhh
coral fog
which is u = x+1/2
white ruin
And then again back to x
coral fog
holyyyy
white ruin
Yesss
white ruin
Haha fair
coral fog
nah idk what to tell you
thanks for your help
without you i think i would've skipped the exercise
topaz sinewBOT
@coral fog Has your question been resolved?
neon iron
How do I factor this into a quadratic I can use the discriminant on?
neon iron
I have to find both possible values for C when y = 3x + C is the equation of two tangents to a circle
neon iron
yeah but there's more terms
bold nebula
Maybe show us the original question? Or what's the equation of the circle?
neon iron
The circle with equation x^2+ y^2 -10x -6y -6 = 0 has two tangents with an equation of the form y = 3x + C. Find both possible values for C
neon iron
Yeah to, somehow solve for C
bold nebula
so
exactly one common point = exactly one solution to the quadratic equation you have
When the quadratic equation has exactly one solution?
neon iron
But it says both values for C
so I'm guessing I have to form a quadratic and solve for c
I just cant work out how to factor all my terms into something workable
bold nebula
Hold on, answer my question
neon iron
When there's one solution its a repeated root or ∆' = 0
neon iron
Ive been okay using it to prove that a line is tangent to a circle, but here im just lost
bold nebula
Notice that you can solve for ∆ (in terms of c) and then ∆ = 0
this way gives two possible values for c
neon iron
But I need to get a form where I have A, B and C
bold nebula
yes
neon iron
thus far I only have 10x^2 +6xc -28x -6c -6 + c^2 = 0
neon iron
yeah that was an earlier error
I didnt collect the -6(3x) and -10x
-10x comes from the original circle equation, I just combined them into -28x
neon iron
oh, im just using the whole quadratic in terms of c as the C in discriminant
bold nebula
in penultimate line
bold nebula
yes, coefficients are (lemme use C as the variable we're looking for):
a = 10
b = 6C - 28
c = C^2 - 6C - 6
∆ = b^2 - 4ac = 0
---> C = ...
neon iron
ahhh yeah that's helped a ton, I just didn't realise I could use the rest of the terms as c
lemme work it out real quick
yeah so comes out with -4c^2 -96c + 1024
bold nebula
great
neon iron
thank you, I was making it so much more complicated than it needed to be lol
tysm 😄
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
neon iron
Looking to make sense of something otherwise that comes accross as simple:
"In 40 years, Imran will be 11 times as old as he is now. How old is he right now", the answer is 4 years old.
neon iron
I'm stuck because
he could be 10 and in 40 years if he's 11 times as old as he is now he could be 110 because 10 * 11 = 110.
so why is 4 the definite answer and not ANY other number?
please.
oh because its 40 years and 11 times as old...
I think I got it, sorry for the bother.
.close
topaz sinewBOT
empty sail
he could be 10 and in 40 years if he's 11 times as old as he is now he could be ...
You're misunderstanding it. It's saying that in 40 years, he would be 11 times as old
neon iron
yeah I just noticed, thank you so much for verifying though lol
topaz sinewBOT
Available help channel!
dapper plover
A five-storey building with a square foundation has a total usable floor area of 6480-m^2. The outer walls are 0.5m thick. Find the outside dimensions of the foundation.
Why does it equal 37x37?
topaz sinewBOT
A five-storey building with a square foundation has a total usable floor area of...
empty sail
A five-storey building with a square foundation has a total usable floor area of...
What did you get?
dapper plover
What did you get?
Im getting 38x38 because I assume that after you do 6480/5 = 1296 you square root it in which you get 36 and because there are 4 walls you would do 0.5 x 4 + 36
empty sail
You were close, you don't need to do (0.5 * 4) because it's a square, you only need to do (0.5 * 2)
Basically that's your diagram
One side is x + 1
dapper plover
ohh so you need to extend 0.5 twice to reach your
empty sail
The other is x + 1 as well because it's a square
dapper plover
proper answer
dapper plover
Basically that's your diagram
because the difference between the inside square and outisde would be one because you need to extend both sides of the line by 0.5 right
empty sail
Yes
topaz sinewBOT
topaz sinewBOT
Available help channel!
cinder oxide
topaz sinewBOT
https://youtu.be/b2ZFpE_yrLg?si=a810dhgdZGAgBwiQ&t=5322
cinder oxide
I don't understand what is being demonstrated here @ 1:28:42
distributing the 2, to get +C or +2C
both are exactly the same? or is there some error here
wouldn't it be:
2(x^2/2 + C)
or
x^2 + 2C
not x^2 + C
because, to my understanding, x^2 + 2C and x^2 + C are not the same thing..
rapid marten
So why not change 2C to a new constant C
cinder oxide
you could write x^2 + 243543565657657C and it would be the same thing as x^2 + C?
knotty ledge
What you call the constant doesn't matter, so you may aswell just keep calling it C no matter what happens to it
rapid marten
Ok
cinder oxide
both are the same?
rapid marten
so now we have 2C
cinder oxide
these are both exactly the same?
cinder oxide
it looks different to me
rapid marten
its like overwrites itself
cinder oxide
we only distributed the 2 to the first term
rapid marten
ok imagine
it ist +C its +A
so you have 2(x^2/2 + A)
x^2 + 2A
make C = 2A
now its x^2 + C
it like doesnt really matter
its a constant
cinder oxide
I don't think I understand the concept of C.. i thought it was up or down the y axis
knotty ledge
He literally explains this in the video
empty sail
It's because it's a constant, if you take the derivative of a constant , it becomes 0. So whether you take the derivative of C or 2C, it's still going to be 0
rapid marten
^
cinder oxide
2C and 1C would be different scalars up and down the y-axis, no?
like whatever your constant is, you multiply that by 2, or by 1
empty sail
You're overthinking it tbh
cinder oxide
i'm not understanding why we can't say +2C
technically that would still be correct?
cinder oxide
It's because it's a constant, if you take the derivative of a constant , it beco...
oh right, constant is always 0
rapid marten
You can say 2C if you really wanted too
empty sail
You can but to make life easier, it simplifies to just C.
cinder oxide
You can but to make life easier, it simplifies to just C.
interesting..
knotty ledge
You just care about the fact a constant is there, and is arbitrary
empty sail
You can say 2849274929188C but it's unnecessary to say that because you know the derivative of a constant is 0, so instead of that long number, you can just swap it out and just use C
knotty ledge
As C varies over R, you capture all the same constants whether you write just C or you write 2C or 2849274929188C
cinder oxide
does abosultly nothing useful
lol, I'm gonna start added +549857435847C to all of my answers, see if they mark it wrong on exam
if they do, I will argue it's the same thing
rapid marten
lol, I'm gonna start added +549857435847C to all of my answers, see if they mark...
they'll just think your special
cinder oxide
so it depends on the context.. like here I can't just put a random scalar in front of C
if someone tells me yes, I can make this C into 2324354532C I will be extremely shocked
knotty ledge
That is the letter c being used in a different context
Remember letters get used for different things
cinder oxide
maybe +b would have been better for indefinite integrals, to stick with this same naming convention
f(x) = mx + b
because +b suggests the y-axis, for both I do believe?
knotty ledge
Newsflash not everyone in the world uses mx + b CHRIST
cinder oxide
Newsflash not everyone in the world uses mx + b CHRIST
what would they use instead? i thought f(x) = mx + b would be universal math knowledge from the earlier years before calculus
empty sail
but I thought it was always taught like this?
In America it is taught with m and b
golden mesa
kx+n 💀
empty sail
I use y = λx + θ
knotty ledge
You got an issue with Slovenia and Serbia
golden mesa
i also have a problem with sweden using other
empty sail
i also have a problem with sweden using other
Well Sweden, Slovenia, and Serbia has a problem with you
knotty ledge
Honestly saying "the line Other" is a bit strange
cinder oxide
i also have a problem with sweden using other
Google "Sweden King Hats"
golden mesa
other includes stuff like mx+d for japan
spring patrol
I don’t understand what it’s asking
topaz sinewBOT
I don’t understand what it’s asking
@spring patrol Has your question been resolved?
knotty ledge
What are the requirements to be a function
spring patrol
All x all has one y?
radiant tapir
All x all has one y?
Yep. And do you see a value in A which has two outputs?
knotty ledge
?? Why are you pinging me and not answering Mellow
knotty ledge
Yep. And do you see a value in A which has two outputs?
This person?
spring patrol
I don’t see their texts
spring patrol
Yep. And do you see a value in A which has two outputs?
Does it have more than 1 output?
radiant tapir
Does it have more than 1 output?
correct. As a hint, what does a map to?
spring patrol
Ohhhhh
radiant tapir
so we have an input that is outputting 2 values, which can't happen with functions
spring patrol
Omg that’s so simple I just skimmed over it and missed that I’m so sorry
Thank you so much I need to read them more clearly 😭
.close
frank narwhal
topaz sinewBOT
frank narwhal
really failing to understand why this is wrong maybe im tired but
sec is r/x which is
√(41)/-√(205)/41
turns into
√(41)/1 * -41/√(205)
√(41) goes into √(205) 5 times
1/1 * -41/5
what did i mess up?
golden mesa
what is your x value? -sqrt(205)/41?
frank narwhal
yep
frank narwhal
ahh
i was basing it off cos theta
in that case itd just be 1/√(5)?
well
actually just √(5)/5 i think
since i have to rationalize it
golden mesa
now, since you're in Q3, you're in the negative x-axis
frank narwhal
so -√(205)/5?
golden mesa
yeah
flint star
I believe this limit does not exist? How would I show this? I am not sure how to begin....
topaz sinewBOT
@flint star Has your question been resolved?
topaz sinewBOT
@flint star Has your question been resolved?
topaz sinewBOT
@flint star Has your question been resolved?
lucid junco
If F(x) denotes an anti derivative then what does F’(x) refer to?
lucid junco
Or is F’(x) the anti derivative and F(x) is a function
radiant tapir
it gets you back to your original equation. derivatives/anti-derivaties are inverse operations of one another, similar to + and -
lucid junco
right
So if F(x) is a function then it’s antiderivative will be F’(x) such that it equals f(x)?
radiant tapir
typically we say something like: Let $f(x)$ be a function. Then the anti-derivative will be $F(x)$. Thus $F'(x) = f(x)$
thorny flameBOT
MellowDramaLlama
radiant tapir
or something like that
fair badge
can anyone help me with this question?
topaz sinewBOT
can anyone help me with this question?
fair badge
frail dove
Question 8 or 9?
fair badge
8
fair badge
i'm not sure if i'm supposed to simplify
fair badge
oh wait if i simplify it correctly the answer should be 2n + 5
lucid junco
I’m confused about the part in red. How do we know to add back the x next to the 5?
topaz sinewBOT
I’m confused about the part in red. How do we know to add back the x next to the...
lucid junco
Oops
It should be x^1/1
Not x^1/x
I know that during normal differentiation for something like 5x the x disappears, so during anti differentiation we add an x to it?
hushed flint
I know that during normal differentiation for something like 5**x** the x disapp...
Integration x^n = x^(n+1)/n+1 , n≠-1
hushed flint
where x is 5 in this case
Integration x^0 = x^1/1
lucid junco
But isn’t it 5^1 right now not 5^0
hushed flint
But isn’t it 5^1 right now not 5^0
I said x^0 not 5^0
radiant tapir
But isn’t it 5^1 right now not 5^0
5 = 5*x^0. That's what Someone_21 is saying
but you have the right idea
lucid junco
Yeah I just realised that if f(x) = a then it’s anti derivative will be F(x) = ax + C
radiant tapir
yep pretty much
lucid junco
Also
For the anti derivative of sinx being -cosx, why do the signs swap
Like
The derivative of sin is cos
But for the anti derivative it becomes -cos
And the derivative of cosx is -sinx but it’s anti derivative is +sinx
But I guess if anti differentiation is the exact opposite then I can kinda see why the signs swap around
hushed flint
d/dx(-cosx)=sinx
-cosx =Integration of sinx
lucid junco
Perfect timing llama I was about to ask a question haha
how can I anti differentiate secx(secx + tanx)?
Should I first expand
to sec^2(x) + secxtanx
Ohhh
Got it
tanx + secx
radiant tapir
then thos are known derivatives
junior acorn
(x^3 + 3)^2
expand it using binomial theorem
junior acorn
simplest way for this is also to just expand it
radiant tapir
(x^3 + 3)^2 = x^6 + 6x^3 + 9. Then just find the antiderivative of each
lucid junco
(x^3 + 3)^2
This was my answer for that by the way, am I correct?
junior acorn
This was my answer for that by the way, am I correct?
yes
lucid junco
simplest way for this is also to just expand it
I get this but how do I antidifferentiate that
do I do it separately for each term?
golden mesa
revise linearity of integrals
lucid junco
What the heck is that
golden mesa
$\int A+B~dx=\int A~dx+\int B~dx$
thorny flameBOT
chlamydia
lucid junco
I just got on anti derivatives the textbook isn’t even using the word integrals yet lol
haven’t been introduced to that notation
junior acorn
But something like 6x/x^2
the x/x^2 becomes 1/x right
lucid junco
Do I do it to the top only?
golden mesa
what do you differentiate to get 1/x
junior acorn
lnx
junior acorn
it's just good to know these standard integrals like 1/x and sec^2 x and stuff
junior acorn
so this simplifies to 1 + 6/x + 9/x^2
golden mesa
I just got on anti derivatives the textbook isn’t even using the word integrals ...
bro barely knows what integration is
lucid junco
bro barely knows what integration is
mate
idk what’s ur problem
I just started anti derivatives like an hour ago
So maybe get off me
golden mesa
it's just good to know these standard integrals like 1/x and sec^2 x and stuff
i was responding to this
golden mesa
exactly because you've barely started
golden mesa
you can integrate the constant?
lucid junco
Yeah
lucid junco
my only guess is something with ln squared but don’t know that one
golden mesa
no
think back to power rule of differentiation
it only doesn't work for 1/x -> lnx
lucid junco
Well the derivative of (x^2)^-1 is -(x^2)^-2
golden mesa
$\frac d{dx}\frac1x=-\frac1{x^2}$
thorny flameBOT
chlamydia
golden mesa
$\int \frac1{x^2}~dx=-\frac1x$
thorny flameBOT
chlamydia
lucid junco
This backwards stuff is confusing me
golden mesa
just try to think about what you differentiate to get the integral
golden mesa
yes
topaz sinewBOT
@viscid furnace Has your question been resolved?
topaz sinewBOT
@viscid furnace Has your question been resolved?
topaz sinewBOT
@viscid furnace Has your question been resolved?
topaz sinewBOT
topaz sinewBOT
Available help channel!
stable shuttle
Hello, I dont understand how log32(2) = 0.2
topaz sinewBOT
Hello, I dont understand how log32(2) = 0.2
stable shuttle
can someone explain to me ?
restive inlet
express 32 as a power of 2
stable shuttle
and can you details 32^0.2 = 2 ?
i m suppose to do without calculator
and i dont understand rational exposan
restive inlet
express 32 as a power of 2
stable shuttle
2^4
restive inlet
no
uncut gale
2^4 is 16
restive inlet
$$\red{\log_{2^5}(2)}$$
is the value where
$$(2^5)^{\red{\log_{2^5}(2)}} = 2$$
i.e
$$(2^5)^{\text{what?}} = 2^{5 \cdot \text{what?}} = 2$$
thorny flameBOT
ℝam()n()v
stable shuttle
what = 0.2
ok i think i get it ty man
coz 5*0.2 = 1 and 2^1 = 2 @restive inlet
?
restive inlet
yes
fluid quiver
Does x=25 ?
topaz sinewBOT
Does x=25 ?
raw mirage
if a and b are parallel, yes
topaz sinewBOT
fluid quiver
.reopen
topaz sinewBOT
✅
safe iris
x = 44+47
topaz sinewBOT
topaz sinewBOT
Available help channel!
cosmic burrow
topaz sinewBOT
cosmic burrow
this is a solution my friend gave me but the teacher said it isn't a good solution
So i was just wondering is there another solution?
my teacher gave me a hint which is split the octagon into 2 triangles and 1 rectangle
but then i was stuck
topaz sinewBOT
@cosmic burrow Has your question been resolved?
cosmic burrow
<@&286206848099549185>
topaz sinewBOT
@cosmic burrow Has your question been resolved?
topaz sinewBOT
@cosmic burrow Has your question been resolved?
proven mist
@forest moth #1155506405969760346 Can you help me??? Please
forest moth
this is a solution my friend gave me but the teacher said it isn't a good soluti...
I don’t see the problem with this solution
topaz sinewBOT
@cosmic burrow Has your question been resolved?
silver stone
hiiiiii
topaz sinewBOT
Available help channel!
Show your work, and if possible, explain where you are stuck.
dense slate
empty sail
<@&268886789983436800>
thorn briar
.close
tall condor
How can I write and graphically represent complex numbers that meet this?
tall condor
i know that z=x+yi but i dont know how to manage the abs value and the i
sweet shard
tall condor
so the radius is 2 and applyied to |z-1| i assume that is a circle with sqrt(3) of radius?
neon iron
this is a method where you don't need to compute the absolute value since you know that the radius is already 4
you only need to find the center of the circle defined by the point z0
note the <4
neon iron
kelp karlo
topaz sinewBOT
kelp karlo
drifting swift
draw a line with 5 points upon it
neon iron
drifting swift
maybe take the length of segment AB as 1 for convenience, or just some variable like a if you are uncomfortable with this WLOG assumptoin.
do you not have microsoft paint
neon iron
maybe take the length of segment AB as 1 for convenience, or just some variable ...
what is wlog
drifting swift
without loss of generality
drifting swift
yes
neon iron
so using that I can put BC in terms of a
and plug that into the 2nd thing
and then put cd in terms of a
and plug that in the final thing
am i going in the right track
drifting swift
yes
neon iron
ok thanks i'll play around with that and get back to you if i'm still stuck
ye got it thanks ann
.close
pseudo sonnet
topaz sinewBOT
pseudo sonnet
!status
topaz sinewBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
4
Just asking for confirmation
a) - subfield
b) - not a subfield
c) - not a subfield
in b), the multiplicative inverse doesn't exist in the subset
and in c), you can multiply 2 elements x,y and get an element not in the subset
at least, I think you can
I'm not entirely sure if I have it right
I'm quite confident that in a), the subset forms a subfield, since 1 is in the subset, additive inverses and multiplicative inverses seem to be, and x+y and xy seem to return elements in the subset
barren lion
what's your example for (c)?
pseudo sonnet
if you take a+bi(sqrt2) and c+di(sqrt2), and then multiply them together, you get (ac-2bd) + (ad+bc)i(sqrt2)
call ac-2bd = E
and ad+bc = F
now we have E + Fi(sqrt2)
but in order for this complex number to be in the subset
F must be rational
however F = ad+bc
barren lion
right
barren lion
you can't just claim it can be irrational, you need a specific example
pseudo sonnet
ok
barren lion
same for (b)
pseudo sonnet
you can't just claim it can be irrational, you need a specific example
okay, I can do that
barren lion
since you naturally get rationals for the multiplicative inverse
yeah, but you still need a counterexample
not just a claim
topaz sinewBOT
@pseudo sonnet Has your question been resolved?
neon iron
topaz sinewBOT
https://i.imgur.com/Q6ix8nw.png
neon iron
How do I find r in this scenario?
I genuinely have no real idea how
(got help in a forum cause im silly and thought i deleted it lmao)
.close
maiden wave
topaz sinewBOT
https://cdn.discordapp.com/attachments/907022262920708158/1155576155945054258/im...
maiden wave
We consider a thin plate occupying region D of the plane described in a). The density of the plate is
inversely proportional to the distance from the origin. Determine the coordinates of the center of mass of the
plate.
This is what i tried
topaz sinewBOT
@maiden wave Has your question been resolved?
topaz sinewBOT
@maiden wave Has your question been resolved?
maiden wave
<@&286206848099549185>
tawny surge
Are you just struggling with the integral?
maiden wave
i guess, but maybe its impossible to solve it because i made a mistake while making it
tawny surge
double check?
tawny surge
how did you make the integral>
maiden wave
Check
Plug in the formula
K/r^2 is the density
@tawny surge
mass/area
Then when u do the integgral youre left with only mass
nobody wants to help me :(
topaz sinewBOT
@maiden wave Has your question been resolved?
maiden wave
help me please :)
tawny surge
i don't get why it is 1/r^2
"inversely proportional to the distance from the origin"
so should be k/r, right?
tawny surge
help me please :)
what do you think>
maiden wave
hmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm